Common optical elements such as lenses and prisms are formed from homogeneous masses of transparent materials. Thus, the properties of the material are homogeneous throughout the entire optical element. Although several optical elements formed from different materials can be cemented or otherwise assembled together to form a compound element, the properties of the material within each element of the compound device are still constant. Optical theorists have realized that the performance of optical systems could be materially enhanced if refractive elements could be made with optical properties such as index of refraction and other properties which vary in a preselected fashion from place to place within the optical element. Optical elements having an index of refraction which varies from place to place within the element are referred to as "gradient index" elements and, more generally, optical elements having any property which varies from place to place with the element are referred to as "gradient property" elements.
Various attempts have been made heretofore to manufacture gradient property elements, and particularly gradient index elements. Certain small gradient index elements can be fabricated by exposing a uniform material to a leaching process in which one or more constituents are gradually removed by diffusion from the element into a leaching solution. The reverse approach of exposing the element to a bath or vapor containing an additive so that the additive diffuses into the element can also be used. These surface-based modification techniques require lengthy treatment at elevated temperatures and under controlled conditions to produce even a small gradient in a property over a small region of the optical element adjacent its surface. Accordingly, these techniques have been largely limited to fabrication of very small optical elements such as optical fibers with very small gradients in index of refraction or other properties.
U.S. Pat. Nos. 4,907,864; 4,883,522; and 4,929,065 of Hagerty et al and my own earlier U.S. Pat. No. 5,044,737 disclose fundamental advances in manufacture of gradient property optical elements including gradient index elements. The disclosures of these patents are hereby incorporated by reference herein. These patents disclose manufacture of optical elements by assembling starting materials of non-uniform composition to form a starting assemblage having different compositions at different locations in the assemblage. For example, glass plates of different compositions may be stacked one atop the other to form the starting assemblage. In an analogous manner, the starting assemblage may include a mass incorporating glass frits or powders of various compositions arranged so that the different compositions are located at different points. That starting assemblage is then subjected to a diffusion process, typically at elevated temperature, so as to fuse the various starting materials into a solid mass, commonly referred to as a "blank" which can either be used directly as an optical element, or, more preferably, ground to a desired shape or otherwise treated to fashion it into a finished optical element. During the diffusion process, each constituent tends to diffuse from regions of the assemblage where it is at a high concentration to where regions where it is at a lower concentration. Thus, after the diffusion process has operated for a finite time, the resulting blank has a smooth gradation in composition and hence has optical properties which vary smoothly from point to point within the blank. Because the processes taught by these patents do not depend upon diffusion to or from the surface of the blank, they can be used to form blanks, and hence optical elements, of essentially unlimited size and with substantial gradients in optical properties. The processes taught in these patents accordingly represent major advances in the art of fabricating gradient property optical elements, and provide gradient property optical elements which were not previously available.
Despite these major advances in the art, there have been needs for still further improvements. The distribution of optical properties resulting from the assemblage-diffusion process of these patents, if conducted under controlled conditions, will be the same on each repetition using an identical starting assemblage having an identical distribution of constituents. For example, if a series of plates having different compositions are stacked atop one another, and subjected to the same diffusion conditions, the resulting body will have a particular distribution of index of refraction. If identical plates are used in another repetition under identical diffusion conditions, the resulting body will have the same distribution of index of refraction. The process accordingly is repeatable. However, there is no simple relationship between the starting distribution of constituents and the final distribution or pattern of variation of optical properties throughout the resulting product. Thus, the correct pattern has been selected by "cut and try" methods. These methods are laborious and hence expensive. Where only a few pieces are to be produced, the expense of experiments required to find the correct starting distribution of constituents in the assemblage can exceed the cost of actually making the pieces after finding the right distribution.
Where many pieces are to be produced, the initial expense of finding the correct distribution of constituents for the assemblage can be spread over a greater number of pieces and hence becomes less significant. However, a different problem arises in mass production . The starting materials supplied to the process may vary slightly. For example, where glass plates are used to make the assemblage, the composition of one or more of the plates may vary from batch to batch. Such variations require experimentation to find appropriate corrections, such as changes in thickness of the various plates or changes in the diffusion time, to be used in the process so as to correct for the effects of the difference in composition.
Accordingly, there have been needs for improvements in the assemblage-diffusion process as taught in the aforementioned patents which would facilitate selection of the appropriate distribution of compositions in the starting assemblage. As stated in the paper "Gradient Index Glasses of Macro Dimensions and Large Delta n", of Blankenbecler et al, delivered at the International Otto Schott Colloquium of Jul. 23 to Jul. 27, 1990 in Jena, Germany, and later published J. Noncrystalline Solids, Vol. 129, L. 1-3, pp. 109-116 (1991), "The design problem now is to find an achievable initial index distribution n (Z,0) that will yield the desired index profile n(Z,t) (to the accuracy required) after fusing for a time t." Although that paper describes certain relationships for mathematical treatment of the diffusion problem and also mentions the "Lorentz-Lorenz", relation between index of refraction and "density" or concentration of various atoms, it does not disclose an overall method of solving the "design problem."